The European patent application No. 0 018 517 discloses a diagnosis and alarm device for a line data communications network. When the voltage source of a transmission-reception station in the network happens to fail, a predetermined tone alarm signal is generated and transmitted to a central station, over a line normally used for data transmission. The power necessary for the creating of such an alarm tone and for the transmission thereof, is supplied by a back-up voltage source comprised of previously-charged capacitors. Such a system has a number of constraints. Since the physical bulk of the capacitors is a function of the capacitive values thereof, it is preferred to set the values of the capacitors no higher than necessary. Now, this causes the stored energy to be limited, thereby reducing the time length over which the alarm tone can be generated. The receiver to which the alarm is transmitted, must, therefore, be able to detect the presence of a signal that is not a data signal, and identify it within a period of time comparatively short. Discrimination between an alarm signal and a data signal is made possible by choosing the frequency of the alarm signal so that it is out of the data bandwidth. That is why, in a system wherein the data are transmitted within the 800-2500 Hz frequency range, a 350 Hz sinusoidal alarm signal has been chosen. During the time when the alarm is on, the capacitors are progressively discharged and the lowered voltage which results causes the signal which the device could generate to be distorted and therefore include harmonic frequencies of the 350 Hz tone. Some of these harmonics (1050, 1400, 1750, etc.) would be in the data frequency bandwidth. Now, in transmission networks, several stations are often connected to the central station through the same transmission line. In addition, these stations are geographically more or less remotely positioned with respect to the central station toward which the alarm signal is to be sent. As the sending of the alarm tone is purely at random, the chances that the alarm signal generated by a station appears on the line while data is being sent from another station in the network, are important. Any interference between the data and the alarm, therefore, is a hindrance, more particularly, when the alarm tone is 40 db higher than the data because of the remote locations of the data stations with respect to the central station. It is, therefore, necessary to stop the alarm signal generating procedure before this signal is subject to distortion. This has for an effect shortening of the time imparted to the creation of this signal. In order to make the job of the central station devices used to detect the presence of the alarm signal easier it is desirable that, for a given back-up voltage source, the alarm signal be generated for as long a time interval as possible.